Robust adaptive control with rejection to unmodelled dynamics, unknown deterministic disturbance and other bounded disturbances using a new discrete time operator are discussed. It is shown that the adaptive version of the internal model principle can be combined with the relative dead zone to handle more general robust adaptive control problems. With the new operator, it is shown that the design of robust adaptive controller can be simplified and the stabilizability problem of the estimated model can be overcome. Global convergence and stability results are also established for the system without the requirement of persistent excitation. The analysis is supported by simulation results.